We propose a new framework for the optimization of computationally expensive black box problems, where neither closed-form expressions nor derivatives of the objective functions are available. The proposed framework consists of two procedures. The first constructs a global metamodel to approximate the underlying black box function and explores an unvisited area to search for a global solution; the other identifies a promising local region and conducts a local search to ensure local optimality. To improve the global metamodel, we propose a new method of generating sampling points for a wide class of metamodels, such as kriging and Radial Basis Function models. We also develop a criterion for switching between the global and local search procedures, a key factor affecting practical performance. Under a set of mild regularity conditions, the algorithm converges to the global optimum. Numerical experiments are conducted on a wide variety of test problems from the literature, demonstrating that our method is competitive against existing approaches.
Department of Industrial and Systems Engineering, Kent Ridge Crescent, National University of Singapore, Singapore, 119260 July/2013